Blogs about: Mathca

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Supercommutative gaussian integration, and the gaussian unitary ensemble13 comments

Terence Tao wrote 3 months ago: The fundamental notions of calculus, namely differentiation and integration, are often viewed as bei … more →

Tags: Expository, math.PR, math.QA, math.RA, Berezin integration, exterior algebra, gaussian unitary ensemble, Grassmann algebra, Supersymmetry

The Harish-Chandra-Itzykson-Zuber integral formula8 comments

Terence Tao wrote 3 months ago: Let be Hermitian matrices, with eigenvalues and . The Harish-Chandra-Itzykson-Zuber integral formula … more →

Tags: Expository, math.SG, Duistermaat-Heckmann measure, Fourier transform, moment map

1B Midterm Schedule

Danlynn wrote 3 months ago: Jan 25: Econ 101 Feb 1: Econ 102 Feb 11: Math 136 ~*Feb 18-22: Reading Week*~ Feb 25: Math 138 Feb 2 … more →

Tags: University of Waterloo, Midterms, 1B

Update: New Term 1 comment

Danlynn wrote 4 months ago: In the beginning, I was really worried about this term (especially after seeing last terms marks … more →

Tags: University of Waterloo, 1B, Classes, imPRessions, New term

1B Courses & Schedule 2 comments

Danlynn wrote 4 months ago: With the break over and somehow managing to pass all my 1A courses…it is welcome to 1B with si … more →

Tags: University of Waterloo, Courses, Schedule, 1B, Classes

1A Exam Schedule 1 comment

Danlynn wrote 5 months ago: Math 137: Dec. 10 @ 9 a.m. Math 135: Dec. 12 @ 9 a.m. AFM 131 : Dec. 13 @ 9 a.m. CS 115: Dec. 14 @ 1 … more →

Tags: University of Waterloo, 1a, final exam schedule

Walsh's ergodic theorem, metastability, and external Cauchy convergence5 comments

Terence Tao wrote 6 months ago: Two weeks ago I was at Oberwolfach, for the Arbeitsgemeinschaft in Ergodic Theory and Combinatorial … more →

Tags: Expository, math.DS, math.LO, math.OA, ergodic theory, norm convergence, nonstandard analysis, Miguel Walsh, metastability

Some notes on Weyl quantisation10 comments

Terence Tao wrote 7 months ago: One of the basic problems in the field of operator algebras is to develop a functional calculus for … more →

Tags: Expository, math.QA, math.OA, semiclassical analysis, Weyl calculus, Moyal product

Math/CA vs AFM-PA @ Waterloo 10 comments

Danlynn wrote 10 months ago: I can remember my surprise when I found out that I got accepted to both the Mathematical/Chartered A … more →

Tags: University of Waterloo, university, AFM-PA

A cheap version of nonstandard analysis20 comments

Terence Tao wrote 1 year ago: Nonstandard analysis is a mathematical framework in which one extends the standard mathematical univ … more →

Tags: Expository, math.LO, nonstandard analysis, sequential compactness, bolzano-weierstrass theorem

Montgomery's uncertainty principle13 comments

Terence Tao wrote 1 year ago: One of the most fundamental principles in Fourier analysis is the uncertainty principle. It does not … more →

Tags: Expository, math.NT, large sieve, restriction theorem, sieve theory, uncertainty principle

254B, Notes 2: Cayley graphs and Kazhdan's property (T)24 comments

Terence Tao wrote 1 year ago: In the previous set of notes we introduced the notion of expansion in arbitrary -regular graphs. For … more →

Tags: math.SP, math.GR, math.RT, 254B - expansion in groups, property T, Cayley graphs, Mautner phenomenon, spectral gap, Schreier graphs

254A, Notes 4: Building metrics on groups, and the Gleason-Yamabe theorem12 comments

Terence Tao wrote 1 year ago: In this set of notes we will be able to finally prove the Gleason-Yamabe theorem from Notes 0, which … more →

Tags: 254A - Hilbert's fifth problem, math.GR, math.MG, Gleason metric, Gleason-Yamabe theorem, Hilbert's fifth problem, no small subgroups

254A, Notes 3: Haar measure and the Peter-Weyl theorem18 comments

Terence Tao wrote 1 year ago: In the last few notes, we have been steadily reducing the amount of regularity needed on a topologic … more →

Tags: 254A - Hilbert's fifth problem, math.GN, math.GR, math.RT, Abelian Groups, Gleason-Yamabe theorem, Haar measure, locally compact groups, Peter-Weyl theorem

"Introduction to measure theory" now published3 comments

Terence Tao wrote 1 year ago: My graduate text on measure theory (based on these lecture notes) is now published by the AMS as par … more →

Tags: 245A - Real analysis, book, Update, Measure Theory

The inverse function theorem for everywhere differentiable maps24 comments

Terence Tao wrote 1 year ago: The classical inverse function theorem reads as follows: Theorem 1 ( inverse function theorem) Let b … more →

Tags: Expository, math.GN, Inverse Function Theorem, Jean Saint Raymond, Math Overflow

Gleason's lemma4 comments

Terence Tao wrote 1 year ago: This is another installment of my my series of posts on Hilbert’s fifth problem. One formulati … more →

Tags: Expository, math.GR, math.MG, convolution, Gleason metric, Hilbert's fifth problem, no small subgroups

The Cotlar-Stein lemma9 comments

Terence Tao wrote 1 year ago: A basic problem in harmonic analysis (as well as in linear algebra, random matrix theory, and high-d … more →

Tags: Expository, math.FA, almost orthogonality, Elias Stein, Cotlar-Stein lemma

Stein's spherical maximal theorem21 comments

Terence Tao wrote 2 years ago: If is a locally integrable function, we define the Hardy-Littlewood maximal function by the formula … more →

Tags: Expository, Elias Stein, Hardy-Littlewood maximal inequality, spherical maximal function


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